A measurable Lawson criterion and hydro-equivalent curves for inertial confinement fusion

It is shown that the ignition condition (Lawson criterion) for inertial confinement fusion (ICF) can be cast in a form dependent on the only two parameters of the compressed fuel assembly that can be measured with existing techniques: the hot spot ion temperature (T-i(h)) and the total areal density (rho R-tot), which includes the cold shell contribution. A marginal ignition curve is derived in the rho R-tot, T(i)h plane and current implosion experiments are compared with the ignition curve. On this plane, hydrodynamic equivalent curves show how a given implosion would perform with respect to the ignition condition when scaled up in the laser-driver energy. For 3 < < T-i(h)>(n) < 6 keV, an approximate form of the ignition condition (typical of laser-driven ICF) is (T-i(h))(n)(2.6)center dot (n)> 50 keV(2.6)center dot g/cm(2), where (rho R-tot), and (T-i(h)) n are the burn-averaged total areal density and hot spot ion temperature, respectively. Both quantities are calculated without accounting for the alpha-particle energy deposition. Such a criterion can be used to determine how surrogate D-2 and subignited DT target implosions perform with respect to the one-dimensional ignition threshold. c 2008 American Institute of Physics. [DOI: 10.1063/1.2998604]